Currently, applications of the algorithms based on artificial intelligence (AI) principles can be observed in various fields. This can be also noticed in the wide area of electrical drives. Consideration has been limited to neural networks; however, the tasks for the models can be defined as follows: control, state variable estimation, and diagnostics. In the subsequent sections of this paper, electrical machines, as well as power electronic devices, are assumed as the main objects. This paper describes the basics, issues, and possibilities related to the used tools and explains the growing popularity of neural network applications in automatic systems with electrical drives. The paper begins with the overall considerations; following that, the content proceeds with the details, and two specific examples are shown. The first example deals with a neural network-based speed controller tested in a structure with a synchronous reluctance motor. Then, the implementation of recurrent neural networks as state variable estimators is analyzed. The achieved results present a precise estimation of the load speed and the shaft torque signals from a two-mass system. All descriptions in the article are considered in the context of the trends and perspectives in modern algorithm applications for electrical drives.